But surely you can improve the sound quality of the standard system by
installing better speakers.
As long as there is not an impedence mis-match, i don't see a problem.
Indeed, by installing bigger speakers in the front doors you'll improve
bass response and sound quality.
Yes, absolutely (unless the signal is filtered out before it gets there) so gen 1's are ok to put the better speakers into as a first upgrade.
Bigger speakers are better for bass, smaller for treble. Better bigger speakers usually have a smaller separate tweeter built in, as well, I think.